Hilbert–Schmidt Frames: Duality, Weaving and Stability

Document Type : Research Paper


1 Department of Mathematics, Velayat University, Iranshahr, Iran

2 Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

3 Department of Mathematics, Kangnam University, Yongin, Gyeonggi, 16979, Republic of Korea


In this paper, we give some sufficient conditions under which perturbations preserve Hilbert-Schmidt
frames. Also show that the canonical dual of a perturbed Hilbert-Schmidt frame is a perturbation
of the canonical dual (alternative dual respectively) of the original Hilbert-Schmidt frame and dis-
cuss best approximation in the set of all dual Hilbert-Schmidt frames. Next, we apply the woven
principle to Hilbert-Schmidt frames and study the stability of weaving Hilbert-Schmidt frames under
perturbations. Finally, we present sufficient conditions under which perturbations preserve weaving
Hilbert-Schmidt frames and weaving dual Hilbert-Schmidt frames.